Tropical Weyl group action via point configurations and \(\tau\)-functions of the \(q\)-Painlevé equations

DOI10.1007/s11005-006-0052-zzbMath1118.39007OpenAlexW2037525289MaRDI QIDQ867311

Teruhisa Tsuda

Publication date: 15 February 2007

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-006-0052-z

zbMATH Keywords

Weyl groups\(\tau\)-functions\(q\)-Painlevé equationtropical representations

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Difference equations, scaling ((q)-differences) (39A13) Simple, semisimple, reductive (super)algebras (17B20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

Universal character and \(q\)-difference Painlevé equations ⋮ Lattice equations arising from discrete Painlevé systems. I. (A2 + A1)(1) and (A1+A1′)(1) cases ⋮ Quantum representation of affine Weyl groups and associated quantum curves ⋮ Cluster integrable systems, \(q\)-Painlevé equations and their quantization ⋮ Tropical representation of Weyl groups associated with certain rational varieties ⋮ A geometric approach to tau-functions of difference Painlevé equations

Cites Work

• Universal characters and \(q\)-Painlevé systems
• \(q\)-Painlevé VI equation arising from \(q\)-UC hierarchy
• Universal characters and an extension of the KP hierarchy
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• \(q\)-Painlevé systems arising from \(q\)-KP hierarchy
• Discrete dynamical systems with \(W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})\) symmetry
• On a novel \(q\)-discrete analogue of the Painlevé VI equation
• Tau functions of \(q\)-Painlevé III and IV equations
• ₁₀E₉solution to the elliptic Painlev  equation
• Cellular automata and ultra-discrete Painlevé equations
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